Namaste in today's class, we will be solving one of the most interesting questions from geometry. It is related to circle. The most complex side of this question is the construction if the figure provided in the question is well, compared to a cyclic quadrilateral, our solution gets easy, and we will be doing same here. If you are not the member of my channel, I would genuinely like to have you a member of my channel.
So please subscribe the channel and share the video to maximum to benefit all of us. Moving ahead, let's have an overlook on the question. A d is given perpendicular to bc. And CE is given perpendicular to a b. These perpendiculars will be our major get through for today's question. Okay, you know, we always start with a clean and clear figure then mention the information from the question as I have already said, perpendicular lines given are vital.
We construct a circle here assuming ac as a diameter, which is making 90-degree angles at point. E and point. D. You might know one of the. Property of diameter that is, it makes 90-degree angles on the circumference of the circle. Now we can flow with steps easily with the help of statement reason table.
First inside the circle angle DAC, plus angle. DAE is equal to angle BAC being total angle. In addition, two angles, standing on the arc, CD are angle c. E, d and angle. D, a c. So they are always equal similar to statement. Two, two angles, standing on the arc. D. E, are angle DC.
E and angle. D, an e. So they are also equal if we add statements 2. And 3 we can write angle c. E, d, plus angle. Dc. E is equal to angle DAC, plus angle DAE. Now if we see the right-hand side of statement 4, it is same as statement 1. So we replace angle DAC, plus angle, DAE by angle, BAC and form.
The statement 5 as angle c. E, d, plus angle. DCE is equal to angle BAC, carefully, observing the triangle, c. E, d, we can say that angle, c. E, d, plus angle. D, c. E is equal to angle b, d. E, as we know that exterior angle b, d. E, in a triangle is equal to the sum of opposite interior angles. Angle c, e, d and angle. D, c. E, finally, in the statements 5 and 6 left-hand sides are same.
Therefore, we can conclude right? Hand. Sides, also, equal that is angle. B. D. E is equal to angle BAC here. We complete today's solution. I hope this video helped you to clarify your curiosity.
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